$\int t^{12}\,dt=$ $+C$
Answer: The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int t^{{12}}\,dt&=\dfrac{t^{{12}+1}}{{12}+1}+C \\\\ &=\dfrac{1}{13} t^{13}+C \end{aligned}$ In conclusion, $\int t^{12}\,dt=\dfrac{1}{13} t^{13}+C$